Question

Is there an API to get a word’s category?
e.g.,

word: "joke"; caetgory (retrieved from API) : "Entertainment",
word: "united states"; category(retrieved from API): "countries"
word:"jay leno"; category"celebrities(retrieved from API)", 
and so on...

Answer 1

Categorization is always highly subjective. If you wish to use mainstream appproaches, try Wordnet (http://wordnet.princeton.edu/). It’s used by most workers in Natural Language Processing. Here’s an example

dog, domestic dog, Canis familiaris
    => canine, canid
       => carnivore
         => placental, placental mammal, eutherian, eutherian mammal
           => mammal
             => vertebrate, craniate
               => chordate
                 => animal, animate being, beast, brute, creature, fauna

Here’s what you get for “joke”

# S: (n) joke, gag, laugh, jest, jape (a humorous anecdote or remark intended to provoke laughter) "he told a very funny joke"; "he knows a million gags"; "thanks for the laugh"; "he laughed unpleasantly at his own jest"; "even a schoolboy's jape is supposed to have some ascertainable point"

    * direct hyponym / full hyponym
    * part meronym
    * direct hypernym / inherited hypernym / sister term
          o S: (n) wit, humor, humour, witticism, wittiness 
                  (a message whose ingenuity or verbal skill or 
                    incongruity has the power to evoke laughter)

Note that “hypernym” is a broader term and can be used as a category.

For people you can try Wikipedia and scrape the infobox (not much fun – I have spent a lot of time doing it). Better to try DBPedia.

Here is the Wikipedia infobox for Jay Leno:

JayLenoJul08.jpg
Leno in July 2008
Birth name  James Douglas Muir Leno
Born    April 28, 1950 (1950-04-28) (age 60)[1]
New Rochelle, New York, U.S.[1]
Medium  Television
Nationality     American
Years active    1973–present
Genres  Observational comedy
Subject(s)  Everyday life, American culture
Influences  Johnny Carson, Robert Klein, Alan King, George Carlin, Don Rickles, Bob Newhart, Rodney Dangerfield
Influenced  Dennis Miller[2]
Spouse  Mavis Leno (1980–present)
Notable works and roles     The Tonight Show with Jay Leno (host, 1992–2009)
The Jay Leno Show
(host, 2009–2010)
The Tonight Show with Jay Leno (host, 2010– )
Signature   Jay Leno Autograph.svg
Website     The Tonight Show with Jay Leno
Emmy Awards
Outstanding Variety, Music or Comedy Series
1995 The Tonight Show with Jay Leno

I don’t know whether that has been captured for DBPedia. If so you will get some good categorization